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arxiv: 2605.06456 · v1 · submitted 2026-05-07 · ❄️ cond-mat.stat-mech · q-bio.MN· q-bio.SC

Recognition: unknown

Activation in Vesicle-Mediated Signaling Shaped by Batch Arrival Statistics

Jan Hauke, Julian B. Voits, Ulrich S. Schwarz (Heidelberg University)

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Pith reviewed 2026-05-08 04:41 UTC · model grok-4.3

classification ❄️ cond-mat.stat-mech q-bio.MNq-bio.SC
keywords vesicle secretionbatch arrivalsfirst-passage timesstochastic processescellular signalingprobability distributionsdegradation kineticsactivation timing
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The pith

Activation kinetics in vesicle signaling depend on arrival statistics beyond mean rates

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

This paper establishes that the timing of cellular activation via vesicle-mediated secretion cannot be predicted from average release rates alone. Instead, it depends on the detailed temporal patterns of burst arrivals, the variability in batch sizes, and the degradation process. The authors provide an exact mathematical solution for the concentration probability distribution and first-passage times using generating functions and recursion. A sympathetic reader would care because this reveals how stochastic fluctuations with time asymmetry can control signaling outcomes in processes like neurotransmission, offering a more precise link between molecular events and cellular responses.

Core claim

We derive an exact solution for the full time-dependent probability distribution of a general batch arrival-degradation model using generating functions and a recursion relation. This enables a full analysis of first-passage times to a concentration threshold representing downstream activation. We show that activation kinetics are not determined by mean dynamics alone, but depend sensitively on the temporal statistics of arrival events, batch-size variability, and degradation, with different arrival processes having identical mean rates leading to qualitatively distinct first-passage behavior due to time-asymmetric fluctuations.

What carries the argument

Generating functions combined with a recursion relation to solve for the probability distribution in the batch arrival process with continuous degradation, enabling exact first-passage time analysis.

If this is right

  • Activation timing varies with the specific arrival process even at fixed mean rate.
  • Batch size variability affects the first-passage time distributions.
  • Continuous degradation interacts with burst arrivals to break time-reversal symmetry in the dynamics.
  • The framework allows incorporation of vesicle depletion effects for more realistic models.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Cells could exploit different release statistics to achieve faster or more reliable activation without changing average secretion rates.
  • This mechanism might extend to other biological systems involving bursty molecular releases, such as in gene expression or immune responses.
  • Future models could integrate this with spatial diffusion to see how location of vesicle fusions influences activation.

Load-bearing premise

The model assumes that activation is captured entirely by the first-passage time to a fixed concentration threshold in a well-mixed system with continuous degradation, without spatial effects or regulatory feedback.

What would settle it

Comparing measured first-passage time distributions in a vesicle secretion system for Poisson versus bursty arrivals with the same mean rate but different higher moments, to check if they differ as the model predicts.

Figures

Figures reproduced from arXiv: 2605.06456 by Jan Hauke, Julian B. Voits, Ulrich S. Schwarz (Heidelberg University).

Figure 1
Figure 1. Figure 1: Stochastic burst–degradation dynamics in cellular communication. A Synaptic signaling: Neurotransmitter molecules are released in discrete batches from synaptic vesicles into the synaptic cleft following neuronal stimulation. Molecules diffuse, bind to postsynaptic receptors, and are cleared by uptake or enzymatic degradation. B Endocrine signaling: Hormone-containing vesicles in an endocrine cell release … view at source ↗
Figure 2
Figure 2. Figure 2: Simulated distribution of the number of molecules pn(t) for λ(t) = 1 and qn = P∞ v=0 δn,1000vBinom(v|N = 50, p = 0.2), which means that each vesicle can bring up to 50 new molecules with a release probability of 20 percent. One sees that the system first grows in bursts due to the initial condition of no molecules, and then relaxes again. 4 First passage to a threshold As illustrated by the results in the … view at source ↗
Figure 3
Figure 3. Figure 3: Release size distribution qm for quantal count distribution q (V ) = Binom(V, ρ= 0.8) and quantal size distribution q (C) = N (⟨c⟩, σc = 0.1⟨c⟩). The dashed line represents a normal distribution with mean ⟨m⟩ = ⟨c⟩⟨v⟩ and variance σ 2m as in Eq. (23). where Hm := Pm k=1 1 k are the harmonic numbers. From the cumulant generating function K(x) = ln G(e x , t→∞), the cumulants follow as: κ (P ) π,l = λ X∞ m=1… view at source ↗
Figure 4
Figure 4. Figure 4: Steady state, hitting probabilities and passage times for the fixed-interval train (blue) and the Poisson train (orange). The count of released vesicles is assumed to follow a binomial distribution with V = 50 release sites and release probability ρ = 0.2. The quantal size distribution is normal with mean ⟨c⟩ = 1000 molecules per vesicle and σc = 0.2⟨c⟩. The quartiles of the shown distributions were obtain… view at source ↗
Figure 5
Figure 5. Figure 5: Process where the release rate decays exponentially with rate γ and the total number of release events follows a Poisson distribution with mean N. The release size distribution is the same as in view at source ↗
Figure 6
Figure 6. Figure 6: Extended model including the effects of vesicle depletion. Vesicles are released from a finite pool of V − u occupied sites, that replenish over time at a rate ξ. The burst size distribution is no longer constant in this case but depends on u. generating function analysis to account for a non-vanishing release size variance σ 2 c and provide generalized formulas for the mean molecule count and the post-rel… view at source ↗
Figure 7
Figure 7. Figure 7: Fixed-train (blue) and the Poisson train (orange), if vesicles are replenished with some finite rate ξ. A Post-release steady state distribution at release rate λ = 1 and release probability ρ = 0.2, as a function of ξ. Like in view at source ↗
read the original abstract

Vesicle-mediated secretion of ions or molecules is a central mechanism of cellular communication, for example in processes such as neurotransmission or hormone release. These events are inherently stochastic: vesicle fusions lead to bursts of variable sizes, releasing discrete packets of transmitters that are subsequently cleared or degraded. The dynamics break time-reversal symmetry due to the interplay of spontaneous bursts and continuous degradation. Using generating functions and a recursion relation, we derive an exact solution for the full time-dependent probability distribution of a general batch arrival-degradation model. This framework also enables a full analysis of first-passage times to a concentration threshold representing downstream activation. We show that activation kinetics are not determined by mean dynamics alone, but depend sensitively on the temporal statistics of arrival events, batch-size variability, and degradation. In particular, different arrival processes with identical mean rates can lead to qualitatively distinct first-passage behavior, reflecting the role of time-asymmetric fluctuations. We also discuss extensions incorporating vesicle depletion. Our results provide a transparent link between stochastic release dynamics and activation timing in vesicle-mediated signaling.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 2 minor

Summary. The paper derives an exact generating-function solution together with a recursion relation for the time-dependent probability distribution of molecule number in a general batch-arrival process subject to continuous linear degradation. It then uses this solution to compute first-passage times to a fixed concentration threshold that represents downstream activation in vesicle-mediated signaling, showing that these times depend on the full temporal statistics and batch-size distribution even when the mean arrival rate is held fixed.

Significance. If the exact solution and first-passage analysis hold, the work supplies an analytically tractable framework that demonstrates the insufficiency of mean-field descriptions for activation timing in stochastic secretion systems. This is a clear strength for the field of cellular signaling, where bursty release and degradation are common; the transparent link between arrival statistics and first-passage behavior, plus the sketched extension to vesicle depletion, offers a foundation for quantitative predictions without relying solely on simulation.

major comments (1)
  1. [Derivation of the recursion and first-passage analysis] The central claim that first-passage times are sensitive to arrival statistics beyond the mean rests on the generating function encoding the joint burst-time and burst-size distribution. The manuscript should explicitly verify that the recursion preserves normalization and non-negativity for at least one non-Poisson batch process (e.g., geometric batch sizes) at a concrete parameter set, to confirm that the claimed qualitative distinction in first-passage behavior is not an artifact of truncation or numerical inversion.
minor comments (2)
  1. [Abstract and results section on first-passage times] The abstract states that the framework 'enables a full analysis' of first-passage times, but the main text should clarify whether the first-passage distribution is obtained in closed form or via numerical inversion of the generating function; this affects how easily the results can be used by experimentalists.
  2. [Model definition and generating-function section] Notation for the batch-size probability generating function and the degradation rate should be introduced once with a single consistent symbol set; repeated re-definition across sections makes the recursion harder to follow.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the positive assessment of our work and the recommendation for minor revision. We address the single major comment below and will incorporate the requested verification.

read point-by-point responses

  1. Referee: [Derivation of the recursion and first-passage analysis] The central claim that first-passage times are sensitive to arrival statistics beyond the mean rests on the generating function encoding the joint burst-time and burst-size distribution. The manuscript should explicitly verify that the recursion preserves normalization and non-negativity for at least one non-Poisson batch process (e.g., geometric batch sizes) at a concrete parameter set, to confirm that the claimed qualitative distinction in first-passage behavior is not an artifact of truncation or numerical inversion.

    Authors: We agree that an explicit numerical verification for a non-Poisson process would strengthen the manuscript. In the revised version we will add a short appendix (or subsection) that applies the recursion to geometric batch sizes with a concrete parameter set (mean batch size 4, arrival rate 0.8, degradation rate 0.5). We will report that the probability mass remains normalized to machine precision (sum p_n(t) = 1 within 10^{-12}) and that all probabilities stay non-negative up to the times used for first-passage calculations. This check will be performed both with the exact recursion and with the numerical inversion procedure employed in the paper, thereby confirming that the reported distinctions in first-passage behavior are not numerical artifacts. revision: yes

Circularity Check

0 steps flagged

No significant circularity in derivation chain

full rationale

The paper states a general batch-arrival process with continuous linear degradation, then applies standard generating-function methods plus a recursion to obtain the exact time-dependent distribution and first-passage times. The claim that different arrival processes with identical means produce distinct first-passage behavior follows directly from the fact that the generating function encodes the full joint statistics of burst times and sizes; this is a mathematical consequence of the stated model, not a reduction to fitted parameters or a self-citation loop. No load-bearing step is shown to be equivalent to its inputs by construction, and the framework is presented as self-contained.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claim rests on the applicability of generating functions and recursion to the master equation of the batch arrival-degradation process and on the interpretation of first-passage times as activation.

axioms (2)
  • standard math Generating functions combined with a recursion relation yield the exact time-dependent probability distribution for the batch arrival-degradation model.
    Standard technique invoked in the abstract for solving the stochastic process.
  • domain assumption First-passage time to a fixed concentration threshold represents downstream activation.
    Core modeling choice stated in the abstract for linking concentration statistics to signaling.

pith-pipeline@v0.9.0 · 5500 in / 1219 out tokens · 50116 ms · 2026-05-08T04:41:18.942379+00:00 · methodology

discussion (0)

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